Hi there!
While the board templates are not yet officially available via our API, you should be able to work around this by using the idBoardSource parameter and the keepFromSource one in order to create a new board based on an existing one.
So your call would look like this:
curl --request POST \
--url 'https://api.trello.com/1/boards/?name=BoardName&defaultLabels=true&defaultLists=true&idBoardSource=BOARDID&keepFromSource=cards&prefs_permissionLevel=private&prefs_voting=disabled&prefs_comments=members&prefs_invitations=members&prefs_selfJoin=true&prefs_cardCovers=true&prefs_background=blue&prefs_cardAging=regular&key=yourAPIkey&token=yourToken'
where BoardName is the name you want to give to that new board, and BOARDID is the actual ID of the board that you can retrieve via the API (https://developers.trello.com/reference/#boardsboardid-1).
This will also work if the BOARDID is from a board template :)
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